Vector potential in cavity of arbitrary shape

AI Thread Summary
The vector potential in a resonator satisfies the equation involving orthogonality of modes across different frequencies. This equation remains valid in cavities of arbitrary shapes, although determining the functions A becomes more complex. The challenge lies in the mathematical representation of these functions for non-standard geometries. Despite the increased difficulty, the fundamental principles governing vector potential still apply. The discussion highlights the importance of understanding mode behavior in various cavity shapes.
Tianwu Zang
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we know that vector potential in a resonator satisfies the equation \intA(\lambda)A^{*}(\lambda^{'})dV=4\pic^{2}\delta_{\lambda\lambda^{'}
So how about in cavity of arbitrary shape? Does this equation still valid?
Thanks!
 
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The equation represents the orthogonality of modes of different frequencies.
It would hold in a cavity of any shape, but the functions A would be harder to find.
 

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